Non Mopar Battery Isolator question

My question is why the Honda engine is tied to the vehicle charging system at all. If the Honda is a 20hp GX series with electric start I would expect it to have a 20 amp charging system. Maybe it depends on the engine. And what else is connected to the Honda.

If it was mine I would disconnect the Honda from the vehicle system. I would test the Honda battery and then the charging voltage with the engine running. When that is sorted out I would address why the vehicle is only charging at 12.8 volts.